Solvable model of strings in a time-dependent plane-wave background

TL;DR

This paper presents an exactly solvable string model in a specific time-dependent plane-wave background, enabling explicit quantization and analysis of singularity crossing, with implications for string cosmology.

Contribution

It introduces a solvable string model in a null cosmology background with explicit solutions, facilitating the study of string behavior near singularities.

Findings

The background admits explicit solutions in terms of Bessel functions.

String propagation through the singularity can be smooth under certain conditions.

The model is an exact string theory solution with a dilaton that reduces back-reaction effects.

Abstract

We investigate a string model defined by a special plane-wave metric ds^2 = 2dudv - l(u) x^2 du^2 + dx^2 with l(u) = k/u^2 and k=const > 0. This metric is a Penrose limit of some cosmological, Dp-brane and fundamental string backgrounds. Remarkably, in Rosen coordinates the metric has a ``null cosmology'' interpretation with flat spatial sections and scale factor which is a power of the light-cone time u. We show that: (i) This spacetime is a Lorentzian homogeneous space. In particular, like Minkowski space, it admits a boost isometry in u,v. (ii) It is an exact solution of string theory when supplemented by a u-dependent dilaton such that its exponent (i.e. effective string coupling) goes to zero at u=infinity and at the singularity u=0, reducing back-reaction effects. (iii) The classical string equations in this background become linear in the light-cone gauge and can be solved explicitly in terms of Bessel's functions; thus the string model can be directly quantized. This allows one to address the issue of singularity at the string-theory level. We examine the propagation of first-quantized point-particle and string modes in this time-dependent background. Using certain analytic continuation prescription we argue that string propagation through the singularity can be smooth.